a) The marginal profit MP(x) for producing x units of an electrical appliance is given by the linear function MP(x)%3D80+0.03x where MP(x) is in dollars per unit. Knowing that P 0 when x 0, recover the profit function P. [Hint: P(x)- J MP(x) dx]
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![(a) The marginal profit MP(x) for producing x units of an electrical appliance is given by the
linear function
MP(x) = 80 +0.03x
where MP(x) is in dollars per unit. Knowing that P 0 when x 0, recover the profit
function P. [Hint: P(x)- MP(x) dx]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52477c1a-5eb4-4353-b81a-7eb697c771f5%2F029855cc-1562-45cb-b6c5-dc9d44a1f439%2Fr1n3eb_processed.jpeg&w=3840&q=75)
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- function for the lightweight compasses is given by p = 40- 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Type your answer here:E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudyA factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"
- How to calculate Samsung's cost (C(Q)) of producing 1, 2,...15?suppose the Total Revenue function for a product is given by R(x)=V0•1x+0-2x² (R-4,x--u) a) Find the Rate of change in Tota) Revenue or Morginal Revenue . a) b) Find Margina) Revenue nhen x=4 units are sold and slate nhatitpredicts for the sale of the next unit c) Firid the Actual change in To tol Revenue uhen productm Level is ingeased from 4 to 5 units di Esplainany discreponcy hetncen parls (1) and (c)resuHs mathemohie ally / Graphically d)Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch It
- E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3DUse the information in the graph to the right to find the values for the following at an output level of 35. 100 The marginal cost is S (Enter a numenc response using an integer.) MC ATC AVC 54 38 -- 17 35 PostMarginal Revenue for an Apartment Complex Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -6x² + 1620x - 36000 (a) What is the actual profit realized from renting the 61st unit, assuming that 60 units have already been rented? $ 40,434 X (b) Compute the marginal profit when x = 60 and compare your results with that obtained in part (a). $ 900
- Assume the cost of making 30 belts $800 the cost of makin 35 belts $900 and the cost equation is linear. The belts are sold for$ 27 each. a)find the marginal cost b)find a linear equation in slope-intercept, form that represent the total Cost of making will c) What is the fixed cost? d) find a profit in slope- intercept that will represent the profit if x belt are made and sold? e) Find the break even point?Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changing
